TY - JOUR
AU - Bhattacharya,Jay
AU - Vogt,William B.
TI - Do Instrumental Variables Belong in Propensity Scores?
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 343
PY - 2007
Y2 - September 2007
DO - 10.3386/t0343
UR - http://www.nber.org/papers/t0343
L1 - http://www.nber.org/papers/t0343.pdf
N1 - Author contact info:
Jay Bhattacharya
117 Encina Commons
CHP/PCOR
Stanford University
Stanford, CA 94305-6019
Tel: 650/736-0404
Fax: 650/723-1919
E-Mail: jay@stanford.edu
William B. Vogt
513 Brooks Hall
Department of Economics
Terry College of Business
University of Georgia
Athens, GA 30602
Tel: 706-542-3970
Fax: 706-542-3376
E-Mail: william.b.vogt@gmail.com
AB - Propensity score matching is a popular way to make causal inferences about a binary treatment in observational data. The validity of these methods depends on which variables are used to predict the propensity score. We ask: "Absent strong ignorability, what would be the effect of including an instrumental variable in the predictor set of a propensity score matching estimator?" In the case of linear adjustment, using an instrumental variable as a predictor variable for the propensity score yields greater inconsistency than the naive estimator. This additional inconsistency is increasing in the predictive power of the instrument. In the case of stratification, with a strong instrument, propensity score matching yields greater inconsistency than the naive estimator. Since the propensity score matching estimator with the instrument in the predictor set is both more biased and more variable than the naive estimator, it is conceivable that the confidence intervals for the matching estimator would have greater coverage rates. In a Monte Carlo simulation, we show that this need not be the case. Our results are further illustrated with two empirical examples: one, the Tennessee STAR experiment, with a strong instrument and the other, the Connors' (1996) Swan-Ganz catheterization dataset, with a weak instrument.
ER -